Problem: The sum of two numbers is $114$, and their difference is $6$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 114}$ ${x-y = 6}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 120 $ $ x = \dfrac{120}{2} $ ${x = 60}$ Now that you know ${x = 60}$ , plug it back into $ {x+y = 114}$ to find $y$ ${(60)}{ + y = 114}$ ${y = 54}$ You can also plug ${x = 60}$ into $ {x-y = 6}$ and get the same answer for $y$ ${(60)}{ - y = 6}$ ${y = 54}$ Therefore, the larger number is $60$, and the smaller number is $54$.